Can Customer Arrival Rates Be Modelled by Sine Waves?
Bibliographic record
Abstract
Customer arrival patterns observed in the real world typically exhibit strong seasonal effects. It is therefore natural to ask, can a nonhomogeneous Poisson process (NHPP) with a rate function that is the simple sum of sinusoids provide an adequate description of reality? If so, how can the sinusoidal NHPP be used to improve the performance of service systems? We empirically validate that the sinusoidal NHPP is consistent with arrival data from two settings of great interest in service operations: patient arrivals to an emergency department and customer calls to a bank call centre. This finding provides rigorous justification for the use of the sinusoidal NHPP assumption in many existing queuing models. We also clarify why a sinusoidal NHPP model is more suitable than the standard NHPP when the underlying arrival pattern is aperiodic (e.g., does not follow a weekly cycle). This is illustrated using data from a car dealership and also via a naturalistic staffing simulation based on the call centre. On the other hand, if the arrival pattern is periodic, we explain why both models should perform comparably. Even then, the sinusoidal NHPP is still necessary for managers to use to verify that the arrival pattern is indeed periodic, a step that is seldom performed in applications. Code for fitting the sinusoidal NHPP to data is provided on GitHub. History: This paper has been accepted for the Service Science/Stochastic Systems Joint Special Issue. Funding: N. Chen was supported by Natural Sciences and Engineering Research Council of Canada Discovery [Grant RGPIN-2020-04038]. H. Shen was supported by China Ministry and Science and Technology [Grant 2022SQGH10861], Hong Kong Special Administrative Region University Grants Council Collaborative Research Fund [Grant C7162-20G], University of Hong Kong Budget and Resources Committee Grant, University of Hong Kong Business School, Shenzhen Research Institutes [Grant SZRI2023-TBRF-03].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".